Sixth. Dr. Steinman's estimated costs for substructure not only exceed greatly those of the author, but also the ratios of division thereof between main piers and anchorages are fundamentally different from his.

Seventh. In his cantilever-bridge estimates Dr. Steinman divides the metal into five groups, viz.: Suspended span, cantilever arms, anchor arms, towers, and anchorages, but some of the total amounts for these groups are greatly out of proportion.

Eighth. Dr. Steinman uses an intensity of working stress for wire cables varying with the span length, while the author has employed a constant value, in accordance with his standard practice of varying live loads and impact allowances and keeping the unit stresses unchanged. The effect of this variation would be to shorten somewhat the span-length for equal cost of the contrasted types.

A dissertation upon the first, sixth, and seventh variations may throw some light upon, the subject; and, to make it properly, it became necessary to reproduce here Dr. Steinman's two layouts, as shown in Fig. 13g and Fig. 13h.

Is it not evident from a glance at Fig. 13g that the long anchor arms, passing over dry land, must be uneconomic as compared with steel trestle-work, which, as is well known, is the cheapest kind of metallic structure? It is true that Dr. Steinman, Dr. Burr, and, possibly, other writers have shown mathematically that the economic length of the anchor arm is four-tenths of the main opening;* but such questions cannot be solved by mathematical analysis, for it is impracticable to consider by equations the many variables in the make-up of an anchor arm, as well as simultaneously a trestle approach. Dealing with this point, the author made the following statement in "De Pontibus": "When, however, the problem is to determine the economic length of anchor arm for a fixed distance between main piers, the result will be quite different; because, within reasonable limits, the shorter the anchor arm the smaller will be its total weight of metal, and because trestle approach is much less expensive than anchor arm. It would not, for evident reasons, be advisable to make the length of anchor arm less than twenty per cent of that of the main opening, or, say, fifteen per cent of the total distance between centers of anchorages. With this length there would probably be no reversion of stress in the chords of the anchor arm, even when impact is considered. Generally, though, the appearance of the structure will be improved by using longer anchor arms than the inferior limit."

If there were no other way to settle this question, the author would be willing to determine it beyond all possibility of doubt by preparing actual designs and estimates of quantities and costs for the anchor arm layout

* This is nearly correct for the case where the locations of the anchorages are fixed, while the main piers may be placed where desired; but in Dr. Steinman's study it is the main piers that are fixed in location, hence the assumption made for economic length of anchor-arms is unwarranted.